True or False?

Which of the following statements are true?

1. At least one of these ten statements is false.
2. At least two of these ten statements are false.
3. At least three of these ten statements are false.
4. At least four of these ten statements are false.
5. At least five of these ten statements are false.
6. At least six of these ten statements are false.
7. At least seven of these ten statements are false.
8. At least eight of these ten statements are false.
9. At least nine of these ten statements are false.
10. At least ten of these ten statements are false.

I think the first 5 are true.
#9. If all 10 are false, that's what #10 states.
But, if #10 is true, that's a contradiction since all 10 are not false.
Then, there must be 1 true statement with the remaining 9 not true.
That's what #9 states.